Geological Society of America South-Central Section Conference Bengtson Analysis of Folds In The Central Region of The Ouachita Fold-Thrust Belt Aaron Ball Geological Society of America South-Central Section Conference 4/5/2013

Geologic setting This study focuses on the Boktukola syncline and two associated anticlines Part of the Ouachita Fold & Thrust Belt, SE Oklahoma Central region of Ouachita System between the Boktukola and Windingstair faults Characterized by several broad, north-verging synclines

Introduction

Methods: Bengtson Analysis Cylindrical Folds Conical Folds Adapted from Bengtson 1980

Methods: Mathematica Code No computer program for Bengtson plots I developed code for tangent diagram analysis with Mathematica Used field measurements and published orientation data Part of M.S. Thesis on geometry and placement of syncline

Methods: Mathematica Code

Methods: Mathematica Code CreateBengtsonDiagram module creates background vector graphic PlotBeddingAttitudes module plots data points on background

Methods: Mathematica Code ContourBeddingAttitudes module Grids plot area using method described by Haneberg (2003) Counts data points within a search radius Calculates distance from node to data point If point is within defined search radius then count value increases Finally, assigns count value to grid node for contouring

Methods: Mathematica Code Mathmatica function ListContourPlot generates contour lines from 3D gird Curve fitted to data for analysis Although the hyperbola is best fit curve for conical folds (Bengtson, 1980), the a parabola is used here. Parametric form of parabola can be fitted to data using rotation and translation matrice

Methods: Mathematica Code

Methods: Mathematica Code The linear equation for fitting the parabola in parametric equations: x = a t2 sin(τ ) + 2 a t cos(τ ) + ψ sin(τ ) y = a t2 cos(τ ) – 2 a t sin(τ ) – ψ cos(τ ) Where : τ = trend angle - /2, ψ = plunge angle, a = openness factor of parabola

Methods: Mathematica Code Manipulate function allows user to fit curve to determine trend/plunge and openness of parabola User must interpret contours to determine fold morphology This process equivalent contouring Kalsbeek Counting Net

Methods: Mathematica Code The openness factor (a) of parabola is estimated from contour plot. Cylindrical folds treated as special case of a conical fold with large openness factor (>10) Function for least-squares fitting or minimizing RMSE of parabolic curve is forthcoming

Results: Nunichito Anticline Gently plunging, conical anticline Crestline trend/plunge is 271, 16 Openness factor is 2.5 Best fit curve opens away from origin This indicates vertex is down plunge (type II)

Results: Boktukola Syncline Subhorizontal, conical syncline Crestline trend/plunge is 252, 3 Openness factor is 3 Best fit curve opens toward origin indicating vertex is up-plunge (type II)

Results: Big One Anticline Gently plunging, cylindrical anticline Openness factor is >10 Crestline trend/plunge is 078, 14

Discussion Conical folds form during flexural slip with an element of rotation, which may indicate shear along bounding faults (Becker, 1995) Big One Anticline is cylindrical fold due to decreasing shear along fault; Boktukola and Nunhichito may still have a sense of shear along the fault Mathematica code provides user a rapid way to plot and analyze bedding attitudes Analysis suggests shear along Boktukola fault followed compression This shear may die out along the bend in the orocline

Questions? Becker, A., 1995, Conical drag folds as kinematic indicators for strike-slip fault motion: Journal of structural geology, v. 17, no. 11, p. 1497-1506. Bengtson, C. A., 1989, Structural uses of tangent diagrams: Geobyte, v. 4, no. 1, p. 57-61. Bengtson, C. A., 1981, Comment and Reply on ‘Structural uses of tangent diagrams’: REPLY: Geology, v. 9, no. 6, p. 242-243. Haneberg, W. C., 2004, Computational Geosciences with Mathematica, Springer-Verlag GmbH. Whitaker, A. E., and Engelder, T., 2006, Plate-scale stress fields driving the tectonic evolution of the central Ouachita salient, Oklahoma and Arkansas: Geological Society of America Bulletin, v. 118, no. 5-6, p. 710.